Physical Chemistry Third Edition

818 19 The Electronic States of Atoms. III. Higher-Order Approximations

We have used the identity

sin^2 (θ)+cos^2 (θ) 1

and the fact that

|Φm|^2 Φ∗mΦm

1

2 π

e−imφeimφ

1

2 π

Exercise 19.7

For hydrogen-like orbitals, show that

ψ^22 px+ψ^22 py+ψ^22 pz

is independent ofθandφ, as asserted by Unsöld’s theorem.

PROBLEMS

Section 19.6: Atoms with More Than Two
Electrons

19.27Find the value of〈r〉for a hydrogen-like 2sorbital with
Z 1 .776. Compare it with the value forZ 2 .686.

19.28Using the values for the orbital exponents (effective
number of protons in the nucleus) in Section 19.6, draw
graphs of the radial distribution function for each orbital
in the ground state of the Li atom. Draw a graph of the
total radial distribution function.

19.29Write the ground-state electron configurations by
subshells for the following elements:

a. Fe

b. Rn

c.Tc

d.Rb

19.30Using Hund’s rules, write the ground term symbol for
each of the elements in Problem 19.29.

19.31Using Hund’s rules, write the ground term symbol for
each of the following elements:

a. N

b. S

c.Cr

d.W

19.32Write all of the term symbols for the ground

configurations of the following elements: (a) P, (b) Ca,

(c) Cu, (d) Cl. Omit the values of the quantum numberJ.

19.33Without consulting a periodic table give the electron

configuration and the term symbol for the lowest-energy

term of each of the atoms. The number in parentheses is

the atomic number.

a.Fe(26)

b.Kr(36)

c.N(7)

d.Ag(47)

19.34Without consulting a periodic table give the electron

configuration and the term symbol for the lowest-energy

term of each of the atoms. The number in parentheses is

the atomic number.

a.Cr(24)

b.K(19)

c.S(16)

d.Pd(46)

19.35Explain why each of the following elements has a ground

configuration different from that predicted by the

diagonal mnemonic device: (a) Mo, (b) Ag, (c) Pd.

19.36The ionization potential (energy to remove one electron)

of a sodium atom in its ground state is 5.1 eV. Use this to